The invention relates in general to a method of correcting the measurements of a pressure gauge for the influence of temperature. More particularly, the invention relates to a dynamic correction method making it possible to correct for the effects of rapid variations of temperature (called transients) the measurements provided by a pressure gauge. The invention is particularly applicable to pressure measurements performed by means of a piezoelectric sensor, and it is particularly advantageous for use with measurements performed in boreholes in the oil industry.
It is known that pressure gauges provide measurements that are highly affected by temperature. This is true of pressure gauges that include a resonator made of a piezoelectric crystal, with a measurement being made on the basis of the resonant frequency of the resonator changing as a result of the pressure applied thereto. This is also true of strain gauges such as piezoresistive bridge gauges, including resistors connected in a bridge circuit with the resistances thereof being changed by deformation due to the application of pressure.
U.S. Pat. No. 4,607,530 (Chow) provides a detailed explanation of techniques for eliminating the effect of temperature on pressure measurements, and is devoted more particularly to gauges including a piezoelectric crystal. A conventional technique as described in U.S. Pat. No. 3,561,832 consists in providing a second gauge for use as a reference, with the second gauge being subjected to the same temperature fluctuations as the measurement gauge, but having a constant pressure applied thereto. Once thermal equilibrium is achieved, the difference between the frequencies of oscillation of the two gauges is assumed to give an indication of the difference between the pressures applied to each of the gauges, without Interference from temperature.
For it to be complete, this "static" compensation technique assumes that the gauges are in thermal equilibrium, in other words that all points on the gauges are at the same temperature. Unfortunately, real measurement conditions are often far from equilibrium, in particular when performing measurements in an oil well. Rapid variations of temperature and fluid pressure in the well are very common, for various reasons. For example, if measurement is performed by means of a device being moved along the well to obtain a log (pressure profile as a function of depth), the temperature around the device changes constantly throughout such displacement because of the geothermal gradient, and at common displacement speeds, time is not available for equilibrium to be reached. Alternatively, if the device is placed at a given depth in the well, and is used in tests during which rapid variations are generated in the pressure acting on the gauge, then pressure shocks give rise to adiabatic heating. Under such conditions, the temperature is not uniform at all points on the gauges, thereby causing the above-mentioned compensation to be inaccurate.
To obtain compensation for pressure measurements in the absence of gauge thermal equilibrium, the above-mentioned Chow patent proposes determining the compensation for a piezoelectric crystal gauge on the basis of a dynamic temperature model established on the basis of the pressure measurement and on the basis of a temperature measurement performed in the proximity of the resonator.
A breakthrough was obtained in the field of piezoelectric crystal pressure gauges by the device described in U.S. Pat. No. 4,547,691. That device is remarkable in that the piezoelectric component vibrates simultaneously in two vibration modes that have completely different sensitivity characteristics: one of the modes (mode C) is highly sensitive to pressure, while the other mode (mode B) is most insensitive to pressure, such that the vibration frequency of the second mode is essentially a function of temperature. From the point of view of compensating pressure measurements, the temperature measurements obtained in this way have the advantage of relating to the same piezoelectric component, rather than on its environment as in previously available devices.
It is mentioned in that patent that the vibration frequency in mode C varies with temperature in accordance with the following equation: EQU .DELTA.f/fo=a(T-To)+b(T-To).sup.2 +c(T-To).sup.3 +k(dT/dt)
where To is a reference temperature, dT/dt is the time derivative of temperature, and a, b, c, and k are coefficients. The terms in T-To constitute static correction, whereas the term k(dT/dt) corresponds to the dynamic effect (a transient) that appears during rapid variation of the temperature T of the piezoelectric component.
It has nevertheless been observed, in the situations mentioned above, that the dynamic correction as defined in this way is not entirely satisfactory, since the pressure values obtained clearly continue to have errors that can be attributed to temperature transients.